MHT CET · Maths · Probability
A random variable \(x\) has the following probability distribution. Then value of \(k\) is and \(\mathrm{P}(3 \lt x \leq 6)\) has the value
- A \(\frac{1}{20}, \frac{3}{7}\)
- B \(\frac{5}{21}, \frac{3}{7}\)
- C \(\frac{1}{21}, \frac{3}{7}\)
- D \(\frac{1}{20}, \frac{4}{7}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{21}, \frac{3}{7}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Since } \sum_{x=0}^8 \mathrm{P}(\mathrm{X}=x)=1 \\ & \therefore \quad \mathrm{k}+2 \mathrm{k}+3 \mathrm{k}+4 \mathrm{k}+4 \mathrm{k}+3 \mathrm{k}+2 \mathrm{k}+\mathrm{k}+\mathrm{k}=1 \\ & \Rightarrow \mathrm{k}=\frac{1}{21} \\ & \therefore \quad \mathrm{P}(3 \lt x \leq 6)=\mathrm{P}(\mathrm{X}=4)+\mathrm{P}(\mathrm{X}=5)+\mathrm{P}(\mathrm{X}=6) \\ &=\frac{4}{21}+\frac{3}{21}+\frac{2}{21} \\ &=\frac{9}{21}=\frac{3}{7}\end{aligned}\)
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